2020/10/21 by Joseph E. Lawrence, David E. Manolopoulos
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Boson #Cold Atom Physics and Bose-Einstein Condensates #Computer science #Constraint (computer-aided design) #Discretization #Limit (mathematics) #Mathematical analysis #Mathematics #Path (computing) #Path integral formulation #Physics #Quantum #Quantum mechanics #Quantum, superfluid, helium dynamics #Statistical physics #Sum rule in quantum mechanics #physics.chem-ph
paper · pdf · doi:10.1063/5.0022535
published as J. Chem. Phys. 153, 154113 (2020) · 13 pages, 4 figures
openalex publication_date 2020/10/21 · arxiv created 2020/10/22 · arxiv updated 2020/10/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a simple method for the calculation of reaction rates in the Fermi golden-rule limit, which accurately captures the effects of tunneling and zero-point energy. The method is based on a modification of the recently proposed golden-rule quantum transition state theory (GR-QTST) of Thapa, Fang, and Richardson [J. Chem. Phys. 150, 104107 (2019)]. While GR-QTST is not size consistent, leading to the possibility of unbounded errors in the rate, our modified method has no such issue and so can be reliably applied to condensed phase systems. Both methods involve path-integral sampling in a constrained ensemble; the two methods differ, however, in the choice of constraint functional. We demonstrate numerically that our modified method is as accurate as GR-QTST for the one-dimensional model considered by Thapa and co-workers. We then study a multidimensional spin-boson model, for which our method accurately predicts the true quantum rate, while GR-QTST breaks down with an increasing number of boson modes in the discretization of the spectral density. Our method is able to accurately predict reaction rates in the Marcus inverted regime without the need for the analytic continuation required by Wolynes theory.